Skip to main content
SpringerLink
Log in

Thermo-Poro-Elastic Behaviour of a Transversely Isotropic Shale: Thermal Expansion and Pressurization

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

The Callovo-Oxfordian (COx) claystone is considered as a candidate host rock for a deep geological radioactive waste repository in France. Due to the exothermic waste packages, the rock is expected to be submitted to temperatures up to 90 °C. The temperature rise induces deformations of the host rock, together with an increase in pore pressures, involving complex thermo-hydro-mechanical (THM) couplings. This study aims to better characterize the THM response of the COx claystone to temperature changes in the laboratory. To this end, claystone specimens were tested in a temperature controlled, high pressure isotropic compression cell, under stress conditions close to the in-situ ones. Thermal loads were applied on the specimens along different heating and cooling paths. A temperature corrected strain gage system provided precise measurements of the anisotropic strain response of the specimens. Drained and undrained thermal expansion coefficients in both transversely isotropic directions were determined. The measurement of pore pressure changes in undrained condition yielded the thermal pressurization coefficient. All parameters were analysed for their compatibility within the thermo-poro-elastic framework, and their stress and temperature dependency was identified.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Abbreviations

\(\varepsilon _i\) :

Strain vector containing the 6 independent components of the second rank strain tensor

\(\varepsilon _v\) :

Volumetric strain

\(C_{ij}\) :

Drained compliance tensor in matrix format

\(\sigma _i\) :

Stress vector containing the 6 independent components of the second rank stress tensor

\(\sigma\) :

Isotropic confining stress

\(\sigma '\) :

Terzaghi isotropic effective stress

\(b_i\) :

Biot’s coefficient for i-th direction

\(p_f\) :

Pore fluid pressure

T :

Temperature

\(\alpha _{d,i}\) :

Linear drained thermal expansion coefficient in the i-th direction

\(\alpha _{d}\) :

Volumetric drained thermal expansion coefficient

\(H_{i}\) :

Biot’s linear pore pressure loading modulus in the i-th direction

H :

Biot’s volumetric pore pressure loading modulus

\(K_{d}\) :

Drained bulk modulus

\(K_{s}\) :

Unjacketed bulk modulus

\(\alpha _{u,i}\) :

Linear undrained thermal expansion coefficient in the i-th direction

\(\alpha _{u}\) :

Volumetric undrained thermal expansion coefficient

\(\varLambda\) :

Thermal pressurization coefficient

\(\alpha _{f}\) :

Volumetric thermal expansion coefficient of the pore fluid

\(\alpha _{\phi }\) :

Volumetric thermal expansion coefficient of the pore space

\({\phi }\) :

Porosity

\(K_{\phi }\) :

Unjacketed pore modulus

\(K_{f}\) :

Bulk modulus of the pore fluid

\(\varLambda ^\mathrm{{mes}}\) :

Measured thermal pressurization coefficient

\(\varLambda ^\mathrm{{cor}}\) :

Corrected thermal pressurization coefficient

\(\varLambda _L\) :

Thermal pressurization coefficient of the drainage system

\(V_L\) :

Volume of the drainage system

\(c_L\) :

Compressibility of the drainage system

\(c_f\) :

Compressibility of the pore fluid

V :

Specimen volume

\(\alpha ^\mathrm{{mes}}_{u}\) :

Measured volumetric undrained thermal expansion coefficient

\(\alpha ^\mathrm{{cor}}_{u}\) :

Corrected volumetric undrained thermal expansion coefficient

\(\alpha _{d,i}^*\) :

Elasto-plastic drained thermal expansion coefficient in the i-th direction

\(\alpha _{d,i}^\mathrm{{irr}}\) :

Inelastic drained thermal expansion coefficient in the i-th direction

\(\eta\) :

Ratio between pore water and bulk water thermal expansion coefficients

\(\kappa\) :

Model parameter for the temperature dependency of H

\(\rho\) :

Wet density

\(\rho _d\) :

Dry density

w :

Water content

\(S_r\) :

Saturation degree

s :

Suction

\(\varepsilon _{\mathrm {hyd}}\) :

Hydration swelling

References

  • Abuel-Naga HM, Bergado DT, Bouazza A (2007) Thermally induced volume change and excess pore water pressure of soft bangkok clay. Eng Geol 89(1–2):144–154

    Google Scholar 

  • Andra (2005) Dossier 2005 Argile: evaluation of the feasibility of a geological repository in an argillaceous formation. https://international.andra.fr/sites/international/files/2019-03/3- Dossier 2005 Argile Synthesis-evaluation of the feasibility of a geological repository in an argillaceous formation\_0.pdf

  • Armand G, Bumbieler F, Conil N, de la Vaissière R, Bosgiraud JM, Vu MN (2017) Main outcomes from in situ thermo-hydro-mechanical experiments programme to demonstrate feasibility of radioactive high-level waste disposal in the Callovo-Oxfordian claystone. J Rock Mech Geotech Eng 9(3):415–427

    Google Scholar 

  • Baldi G, Hueckel T, Pellegrini R (1988) Thermal volume changes of the mineral-water system in low-porosity clay soils. Can Geotechn J 25(4):807–825

    Google Scholar 

  • Belmokhtar M, Delage P, Ghabezloo S, Conil N (2017a) Thermal volume changes and creep in the Callovo-Oxfordian claystone. Rock Mech Rock Eng 50(9):2297–2309

    Google Scholar 

  • Belmokhtar M, Delage P, Ghabezloo S, Tang AM, Menaceur H, Conil N (2017b) Poroelasticity of the Callovo-Oxfordian claystone. Rock Mech Rock Eng 50(4):871–889

    Google Scholar 

  • Biot MA, Willis DG (1957) The elastic coefficients of the theory of consolidation. J Appl Mech 24:594–601

    Google Scholar 

  • Bishop AW (1976) The influence of system compressibility on the observed pore-pressure response to an undrained change in stress in saturated rock. Géotechnique 26(2):371–5

    Google Scholar 

  • Blaise T, Barbarand J, Kars M, Ploquin F, Aubourg C, Brigaud B, Cathelineau M, Albani AE, Gautheron C, Izart A, Janots D, Michels R, Pagel M, Pozzi JP, Boiron MC, Landrein P (2014) Reconstruction of low temperature (\(<100 ^{\circ }\)C) burial in sedimentary basins: A comparison of geothermometer in the intracontinental paris basin. Marine Pet Geol 53:71–87

    Google Scholar 

  • Braun P, Ghabezloo S, Delage P, Sulem J, Conil N (2019) Determination of multiple thermo-hydro-mechanical rock properties in a single transient experiment: application to shales. Rock Mech Rock Eng 52(7):2023–2038

    Google Scholar 

  • Braun P, Ghabezloo S, Delage P, Sulem J, Conil N (2020) Transversely isotropic poroelastic behaviour of the callovo-oxfordian claystone: a set of stress-dependent parameters

  • Brochard L, Honorio T, Vandamme M, Bornert M, Peigney M (2017) Nanoscale origin of the thermo-mechanical behavior of clays. Acta Geotechnica 12(6):1261–1279

    Google Scholar 

  • Brown RJS, Korringa J (1975) On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid. Geophysics 40(4):608–616

    Google Scholar 

  • Cheng AHD (1997) Material coefficients of anisotropic poroelasticity. Int J Rock Mechan Min Sci 34(2):199–205

    Google Scholar 

  • Chiarelli AS (2000) Étude expérimentale et modélisation du comportement mécanique de l’argilite de l’Est, Influence de la profondeur et de la teneur en eau. PhD thesis, Université Lille I

  • Conil N, Talandier J, Djizanne H, de La Vaissière R, Righini-Waz C, Auvray C, Morlot C, Armand G (2018) How rock samples can be representative of in situ condition: a case study of Callovo-Oxfordian claystones. J Rock Mech Geotechn Eng 10(4):613–623

    Google Scholar 

  • Coussy O (2004) Poromechanics. J. Wiley and Sons, New York

    Google Scholar 

  • Delage P, Sultan N, Cui YJ (2000) On the thermal consolidation of Boom clay. Can Geotech J 37(2):343–354

    Google Scholar 

  • Derjaguin BV, Karasev VV, Khromova EN (1992) Thermal expansion of water in fine pores. Prog Surf Sci 40(1–4):391–392

    Google Scholar 

  • Escoffier S (2002) Caractérisation expérimentale du comportement hydroméchanique des argilites de Meuse/Haute-Marne. PhD thesis, Institut National Polytechnique de Lorraine

  • Ewy RT (2015) Shale/claystone response to air and liquid exposure, and implications for handling, sampling and testing. Int J Rock Mech Min Sci 80:388–401

    Google Scholar 

  • Favero V, Ferrari A, Laloui L (2018) Anisotropic behaviour of opalinus clay through consolidated and drained triaxial testing in saturated conditions. Rock Mech Rock Eng 51(5):1305–1319

    Google Scholar 

  • Fei Y (1995) Thermal expansion. In: Ahrens TJ (ed) Mineral physics and crystallography: a handbook of physical constants. American Geophysical Union, Oxford, pp 29–44

    Google Scholar 

  • Gaucher E, Robelin C, Matray JM, Négrel G, Gros Y, Heitz JF, Vinsot A, Rebours H, Cassagnabère A, Bouchet A (2004) ANDRA underground research laboratory : interpretation of the mineralogical and geochemical data acquired in the Callovian - Oxfordian formation by investigative drilling. Phys Chem Earth 29(1):55–77

    Google Scholar 

  • Gens A, Vaunat J, Garitte B, Wileveau Y (2007) In situ behaviour of a stiff layered clay subject to thermal loading: observations and interpretation. Géotechnique 57(2):207–228

    Google Scholar 

  • Ghabezloo S, Sulem J (2009) Stress dependent thermal pressurization of a fluid-saturated rock. Rock Mech Rock Eng 42(1):1–24

    Google Scholar 

  • Ghabezloo S, Sulem J (2010) Effect of the volume of the drainage system on the measurement of undrained thermo-poro-elastic parameters. Int J Rock Mech Min Sci 47(1):60–68

    Google Scholar 

  • Ghabezloo S, Sulem J, Saint-Marc J (2009a) Evaluation of a permeability-porosity relationship in a low-permeability creeping material using a single transient test. Int J Rock Mech Min Sci 46(4):761–768

    Google Scholar 

  • Ghabezloo S, Sulem J, Saint-Marc J (2009b) The effect of undrained heating on a fluid-saturated hardened cement paste. Cem Concr Res 39(1):54–64

    Google Scholar 

  • Hart DJ, Wang HF (1995) Laboratory measurement of a complete set of poroelastic moduli for Berea sandstone and Indiana limestone. J Geophys Res 100:741–751

    Google Scholar 

  • IAPWS-IF97 (2008) IAPWS Industrial Formulation 1997 for the thermodynamic properties of water and steam. Springer, Berlin

    Google Scholar 

  • Liu J, Fokker PA, Peach CJ, Spiers CJ (2018) Applied stress reduces swelling of coal induced by adsorption of water. Geomech Energy Environ 16:45–63

    Google Scholar 

  • Martin RT (1962) Adsorbed Water on Clay: A Review. In Clays and Clay Minerals. Elsevier, pp 28–70. https://doi.org/10.1016/B978-1-4831-9842-2.50007-9

  • McKinstry HA (1965) Thermal expansion of clay minerals. Am Mineral 50(1–2):212–222

    Google Scholar 

  • Menaceur H, Delage P, Tang AM, Conil N (2015) The thermo-mechanical behaviour of the Callovo-Oxfordian claystone. Int J Rock Mech Min Sci 78:290–303

    Google Scholar 

  • Menke W (1989) Geophysical data analysis: discrete inverse theory. Academic Press Limited, London

    Google Scholar 

  • Mohajerani M, Delage P, Monfared M, Tang AM, Sulem J, Gatmiri B (2011) Oedometric compression and swelling behaviour of the Callovo-Oxfordian argillite. Int J Rock Mech Min Sci 48(4):606–615

    Google Scholar 

  • Mohajerani M, Delage P, Sulem J, Monfared M, Tang AM, Gatmiri B (2012) A laboratory investigation of thermally induced pore pressures in the Callovo-Oxfordian claystone. Int J Rock Mech Min Sci 52:112–121

    Google Scholar 

  • Mohajerani M, Delage P, Sulem J, Monfared M, Tang AM, Gatmiri B (2014) The thermal volume changes of the Callovo-Oxfordian claystone. Rock Mech Rock Eng 47(1):131–142

    Google Scholar 

  • Monfared M, Sulem J, Delage P, Mohajerani M (2011) A laboratory investigation on thermal properties of the Opalinus claystone. Rock Mech Rock Eng 44(6):735–747

    Google Scholar 

  • Palciauskas VV, Domenico PA (1982) Characterization of drained and undrained response of thermally loaded repository rocks. Water Resour Res 18(2):281–290

    Google Scholar 

  • Popov VL, Heß M, Willert E (2019) Transversely isotropic problems. Springer, Berlin, pp 205–212

    Google Scholar 

  • Rad NS, Clough GW (1984) New procedure for saturating sand specimens. J Geotech Eng 110(9):1205–1218

    Google Scholar 

  • Seyedi D, Armand G, Conil N, Vitel M, Vu MN (2017) On the thermo-hydro-mechanical pressurization in Callovo-Oxfordian claystone under thermal loading. In: Poromechanics 2017-Proceedings of the 6th Biot Conference on Poromechanics, pp 754–761

  • Sulem J, Lazar P, Vardoulakis I (2007) Thermo-poro-mechanical properties of clayey gouge and application to rapid fault shearing. Int J Numer Anal Methods Geomech 31(3):523–540

    Google Scholar 

  • Sultan N, Delage P, Cui YJ (2002) Temperature effects on the volume change behaviour of boom clay. Eng Geol 64(2–3):135–145

    Google Scholar 

  • Tang AM, Cui YJ, Barnel N (2008) Thermo-mechanical behaviour of a compacted swelling clay. Géotechnique 58(1):45–54

    Google Scholar 

  • Valenza JJ, Scherer GW (2005) Evidence of anomalous thermal expansion of water in cement paste. Cem Concr Res 35(1):57–66

    Google Scholar 

  • Wileveau Y, Cornet FH, Desroches J, Blumling P (2007) Complete in situ stress determination in an argillite sedimentary formation. Phys Chem Earth 32(8–14):866–878

    Google Scholar 

  • Wissa AEZ (1969) Pore pressure measurement in saturated stiff soils. J Soil Mech Found Div 95(4):1063–1073

    Google Scholar 

  • Xu S, Scherer GW, Mahadevan TS, Garofalini SH (2009) Thermal expansion of confined water. Langmuir 25(9):5076–5083

    Google Scholar 

  • Zhang F, Xie SY, Hu DW, Shao JF, Gatmiri B (2012) Effect of water content and structural anisotropy on mechanical property of claystone. Appl Clay Sci 69:79–86

    Google Scholar 

  • Zhang CL, Conil N, Armand G (2017) Thermal effects on clay rocks for deep disposal of high-level radioactive waste. J Rock Mech Geotech Eng 9(3):463–478

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire Navier, 6-8 avenue Blaise-Pascal, Cité Descartes, 77455, Champs-sur-Marne, Paris, France

    Philipp Braun, Siavash Ghabezloo, Pierre Delage & Jean Sulem

  2. Andra, Meuse/Haute-Marne Underground Research Laboratory, Bure, France

    Nathalie Conil

Authors
  1. Philipp Braun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Siavash Ghabezloo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pierre Delage
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jean Sulem
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nathalie Conil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philipp Braun.

Ethics declarations

Conflicts of interest

The authors declare that there are no known conflicts of interest associated with this publication.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Braun, P., Ghabezloo, S., Delage, P. et al. Thermo-Poro-Elastic Behaviour of a Transversely Isotropic Shale: Thermal Expansion and Pressurization. Rock Mech Rock Eng 54, 359–375 (2021). https://doi.org/10.1007/s00603-020-02269-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-020-02269-y

Keywords

Search

Navigation